NATO ADVANCED STUDY INSTITUTES SERIES
Proceedings of the Advanced Study Institute Programme, which aims at the dissemination of advanced knowledge and the formation of contacts among scientists from different countries
The series is published by an international board of publishers in conjunction with NATO Scientific Affairs Division
A Life Sciences Plenum· Publishing Corporation B Physics London and New Y ork
C Mathematical and D. Reidel Publishing Company Physical Sciences Dordrecht and Boston
D Behavioral and Sijthoff International Publishing Company Social Sciences Leiden
E Applied Sciences Noordhoff International Publishing Leiden
Series C - Mathematical and Physical Sciences
Volume 14-0rigin ofCosmic Rays
Origin of Cosmic Rays Proceedings ofthe NATO Advanced Study Institute
held in Durham, England, August 26-September 6, 1974
edited by
J. L. OSBORNE and A. W. WOLFENDALE Physics Department, University 0/ Durham, Durham, Eng/and
D. Reidel Publishing Company Dordrecht-Holland / Boston-U.S.A.
Published in cooperation with NATO Scientific Affairs Division
Library of Congress Cataloging in Publication Data
NATO Advanced Study Institute, Durham, Eng., 1974. Origin of cosmic rays.
Bibliography: p. I. Cosmic rays-Congresses. I. Osborne, J. L., ed.
Titte. 11. Wolfendale, A. W., ed. III. QC484.8.N37 1974 539.7'223 75-2436
ISBN-13: 978-94-010-1814-2 DOI: 10.1007/978-94-010-1812-8
Published by D. Reide1 Publishing Company P.O. Box 17, Dordrecht, Holland
e-ISBN-13: 978-94-010-1812-8
Sold and distributed in the U.S.A., Canada, and Mexico by D. Reidel Publishing Company, Inc. 306 Dartmouth Street, Boston, Mass. 02116, V.S.A.
All Rights Reserved Copyright © 1975 by D. Reidel Publishing Company, Dordrecht
Softcover reprint of the hardcover 1 st edition 1975 No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher
TABLE OF CONTENTS
J.L. Osborne
G.R. Burbidge
Sidereal Daily Variations in Cosmic Ray Intensity and their Relationships to Solar Modulation and Galactic Anisotropies
T. Thambyahpillai
Energy Spectrum and Mass Composition of Cosmic Ray Nuclei from 1012 to 1020eV
A.A. Watson
I.L. Rasmussen
H. Reeves
K.O. Thie1heim
14 Ga1actic Propagation of Cosmic Rays Be10w 10 eV J.L. Osborne
Possib1e Exp1anations of the Spectra1 Shape
A. W. Wolfendale
P. Meyer
K. Pinkau
F. Pacini
S .A. Co1gate
Supernovae and the Origin of Cosmic Rays (II), a Model of Cosmic Ray Production in Supernovae
S.A. Co1gate
165
203
221
233
267
335
371
399
425
447
PREFAGE
The cosmic radiation was discovered over 60 years aga and since that time many exciting results have appeared, results of interest to a variety of branches of science, primarily Nuclear Physics, Astrophysics and Geophysics. Perhaps the most basic aspect is the intriguing one of the origin of the radiation and the present publication comprises a reproduction of the lectures on the topic given at the Advanced Study Institute held from August 26 to September 6, 1974 in Durham, England.
We endeavoured to organise the Institute as a School as distinct from a Gonference and the lecturers cooperated to the full in making their contributions very clear and comprehensive. In producing the manuscripts for these Proceedings the lecturers were greatly assisted by the Scientific Secretaries (Research Students from our Department, listed overleaf) and we are very grateful to them for their efforts.
Many members of the Physics Department and staff of St. Mary's College (where participants were accommodated), helped with the organisation and we thank them most sincerely. Our particular thanks go to our Departmental Superintendent, Mr. G.F. Gleveland, for his many contributions to the successful outcome of the meeting. We are grateful to Mrs. S.M. Naylor for her help in preparing this printed version of the Proceedings from the manuscripts.
Durham, October 3, 1974 J.L. Osborne A.W. Wolfendale
Institute Directors:
Physics Department University of Durham, Durham, England
G.R. Burbidge
H. Elliot
G.J. Dickinson
D. Dodds
D.K. French
K. Pimley
A.W. Strong
M. White
D.M. Worral
We are very grateful to the Scientific Affairs Division of NATO for sponsoring this Advanced Study Institute.
LIST OF PARTICIPANTS
Lecturers
Burbidge, G.R., University of California, San Diego Colgate, S.A., New Mexico Institute of Mining and Technology Meyer, P., Chicago Osborne, J.L., Durham Pacini, F., Frascati Pinkau, K., Garching Rasmussen, Lyngby Reeves, H., Saclay Stecker, F.W., Goddard Space Flight Center Stephenson. F.R., Newcastle upon Tyne Thambyahpillai, T., Imperial College, London Thielheim. K.O., Kiel Watson, A.A., Leeds Wolfendale, A.W., Durham
Participants
Arens, M., Amsterdam Ashton, F., Durham Barrett, M.L., Leeds Bazer-Bachi, A.R., Toulouse Bignami, G.F., Goddard Space Flight Center Burn, B.J., I.O.A., Cambridge Capelato, H.V., Saclay Carter, P.D., North London Polytechnic Cetincelik, M., T.N.E.K., Ankara Cherki, G., Saclay Cherry, M.L., Chicago di Cocco, G., Bologna Edelstein, W.A., Glasgow FeIten, J.E., Steward Observatory Frangos, A.C., Athens Fuchs, B., Kiel Goned, A.M.S., Cairo Gregory, J.C., Alabama
x
Grupen, C., Gesamthochschule Siegen Hainebach, K.L., Rice University Hermsen, W., Leiden Hillas, A.M., Leeds Jokisch, H., Kiel Juliusson, E., Chicago Karr, G.R., Alabama Kidd, J.M., Naval Research Laboratory, Washington Kinaci, S.R., Ege Universy Lindstarn, S., Lund Linsley, J., University of New Mexico Mandolesi, N., Bologna Martin, J.W., University of Washington Mclvor, I., D.A.M.T.P., Cambridge Meikle, W.P.S., Glasgow Meneguzzi, M., Saclay Moyano, C.E., Garching Nelson, A.H., Cardiff Nissen, D., Kiel O'Sullivan, C.T.O., Cork Paizis, C., Milan Pizzichini, G., Bologna Plieninger, T., Heidelberg Robba, N., Palermo Robson, E.I., Queen Mary College, London Rothermei, H., Garching Sacco, B., Palermo Schlickeiser, R., Kiel Schmidt, W., Garching Schwartz, S.J., D.A.M.T.P., Cambridge Simon, M., Garching Skilling, J., D.A.M.T.P., Cambridge Sun, M.P., Imperial College, London Thompson, M.G., Durham Turner, T., M.E.T.U., Ankara Turtelli, A., Jr., Unicamp Turver, K.E., Durharn Valtaoja, E.J.J., Turku Verrna, S.D., Louisiana Wdowczyk, J., Lodz Westergaard, N.J., Lyngby Wi ld, P., Leeds Wilson, A.S, Sterrewacht te Leiden
LIST OF PARTICIPANTS
INTRODUCTORY COSMIC RAYS
Physics Department, University of Durharn, U.K.
1. SCOPE OF THE PRESENT WORK
The his tory of cosmic ray studies is one of the romances of modern science. From the observations of a small residual ionization in carefully shielded ionization chambers at the turn of the Century sprang the development of a subject embracing many disciplines of physics and leading to fundamental advances in knowledge in many areas.
Despite the identification of the particles present in the cosmic ray beam and a host of measurements on the energy spectra of the components and of the manner in which the particles propagate through the atmosphere and below ground the origin of the bulk of the primary particles is still unclear. Only at 'low' energies, below about a GeV has it been possible to identify the sun as a source of some of the particles. The subject of solar cosmic rays, a topic of great interest, can be regarded as a subject in its own right and attention will not be given to it here; instead, the origin of those components, largely of higher energy and coming from more distant sources, is our prime concern.
It is necessary to state rather clearly what is known about the various primary components and also about Galactic and Extra-galactic space before endeavouring to suggest specific origin models. The first Chapter gives a very brief introduction to the question of the primary components; later Chapters give much more detail and deal with the Astronomical setting.
J. L. Osborne and A. W. Wolfendale (eds.), Origin ofCosmic Rays, l-12.All Rights Reserved. Copyright © 1975 by D. Reidel Publishing Company, Dordrecht-Holland.
2 A.W.WOLFENDALE
1. Definitions
The term 'primary' component is taken to mean the component present above the atmosphere, that is before any secondary inter­ actions in the gas of the atmosphere have taken place. In view of the presence of the earth's magnetic field the intensity of the charged particles will depend on the latitude; when the 'primary spectrum' is quoted, corrections have usually been applied to allow for this field and the spectrum then refers to what would have been observed were the earth's field switched off.
An idea of which particles might be expected to be present in the primary beam comes from an analysis of the 'universal abundances' - data which come from studies of stellar spectra, meteorites, etc. These abundances include a wide variety of nuclear masses with hydrogen as the biggest component; the expec­ tat ion is borne out with the cosmic ray beam being mainly populated by protons, at least at energies below about lOl3eV where direct measurements of primary masses have been made. There are notable differences between the concentrations of various elements in the primary beam and the Universal abundances, however. Some of these are probably due to the cosmic rays at their places of acceleration (the so-called primordial particles) not being representative and others are certainly due to propagation effects. The significant flux of Li, Be and B in the primary beam is virtually certain to be due to the fragmentation of heavier nuc1ei in their passage through interstellar matter.
In addition to the nuclei, primary electrons and positrons have been identified, as have y-rays. Neutrinos and some neutrons will also be present but these have not, as yet,been identified.
2. Energy Density
Some idea of the astrophysical significance of the various components present can be gauged from their energy densities and values are given in Table I. For comparison, energy densities near the earth of other components (visible light, etc.) are also shown.
INTRODUCTORY COSMIC RA YS
Component Energy Density (eV cm-3)
Charged primaries above 10geV 'V 5.10-1 (from summary by 1012eV 'V 2.10-2 Wolfendale, 1973) 1015eV 'V 10-4
1018eV 'V 10-8
E1ectrons and above 10geV 'V 4.10-3 positrons 1010eV 'V 1.10-3 (from summary spec- 10 11 eV 'V 2.10-4 trum of Meyer, 1971)
y-rays, diffuse above 107eV 'V 1.10-5 background above 108eV ~ 2.10-6 (from summary by Strong et a1., 1974)
Starlight 'V 4.10-1 (from Allen, 1974)
2.7K B1ack body 2.4.10-1 radiation
Tab1e I: Energy Densities of 'Cosmic' Components near the Earth ca1cu1ated from the expression
cr = 4; I j(E) EdE, where j(E) is the differential
energy spectrum of the appropriate component. By 'charged primaries' is meant protons and heavier nuc1ei.
3
Examination of the cosmic ray components a1one, above the same energy, say 10geV, shows that there is a wide disparity between their energy densities. Thus, with respect to the charged primarie~ (by which is meant protons and heavier nuc1ei) the e1ectrons and positrons carry about 10-2 of the energy and the diffuse y-ray background carries % 10-7 of the energy. At this point it shou1d be remarked that, for y-rays, there is also a component carrying more energy which is of ga1actic origin; that this is ga1actic is shown by the fact that there is a very broad peak towards the ga1actic centre (with a width in longitude of very approximate1y ± 400 ; Fichte1 et a1., 1973). However, the increase in y-ray energy density is probab1y 1ess than an order of magnitude.
A1though there is a disparity between the energy densities of the individual cosmic ray components, rather remarkab1e near-
4 A. W. WOLFENDALE
coincidences occur between the value for charged primaries (~ 5 x 10-leV cm-3) and some energies relevant to the galaxy. Thus, the energy density of starlight is ~ 4 x lO-leV cm-3 and that associated with the galactic magnetic field is ~ 6 x 10-leV cm-3 for a me an field of 5~gauss (actually the mean field is probably uncertain to a factor 2 and therefore the energy density to a factor 4). Furthermore, the energy density associated with the motions of gas clouds in the galaxy, averaged over the nearby galactic region, is also in the range (1-10) x lO-leV cm-3 Such near agreement is suggestive of an equilibrium situation for a system in which the bulk of the cosmic rays or~g~nate in galactic sources but there can be no certainty about it. For example, the black body radiation also has the same order of energy density (2.4 x 10-leV cm-3) and this radiation is not of galactic origin but almost certainly pervades the whole Universe.
3. Energy Spectra
Although later Chapters will deal with the energy spectra in much greater detail a brief summary is given here.
1~
10 1012 Energy/nucleon
Fig. 1: Summary of measurements on the primary spectrum of protons and nuclei corrected for geomagnetic effects. The summary is that given by Wolfendale (1973) modified to allow for more recent data which indicate that the iron spectrum probably has a somewhat smaller exponent than the other components.
The groupings of nuclei are as folIows: L: 3 ~ Z ~ 5; M: 6 ~ Z ~ 9 and H: 10 ~ z.
INTRODUCTORY COSMIC RA YS
Figure 1 gives a rather superficia1 summary of measurements on the primary spectrum of protons and nuc1ei; the ranges of nuc1ear charge corresponding to L (light), M (medium) and H (heavy) are given in the caption. Nuc1ei of charge much above 26 have also been observed but there are insufficient data as yet to give a good energy spectrum (what evidence there is does not suggest much of a difference from that of the other heavy nuc1ei). Re1ated to the f1ux of the iron grou7, the heaviest nuc1ei, with Z > 96, have a f1ux of about 5 x 10- (B1andford et a1., 1971).
As can be seen in Figure 1 there is some evidence for the spectrum of the H-group being somewhat f1atter than that of the other components. In fact, there is a suggestion that a number of groups of nuc1ei have a sma11er exponent than that of protons For examp1e, Ba1asubrahmanyan and Ormes (1973) quote differential exponents of 2.56 ± 0.04 for carbon and oxygen, 2.44 ± 0.07 for 10 < Z < 14 and 2.0 ± 0.14 for iron, the energy range in each case being about 1-100 GeV/nuc1eon. These exponents can be com­ pared with the va1ue of 2.6 - 2.7 for protons and a-partic1es.
/' )p 0'
.!:'"\ e+e \ I Satell o , 1 _~ 11\""18 IWs \1
v --""'1 11 'I;;
\ \
5
Fig. 2: Summary of measurements of some of the primary components. Protons and a's as in Fig. 1, e+ + e- and y are from the references given in Tab1e I.
6 A.W.WOLFENDALE
Extending the region of interest to higher energies, Figure 2 shows the whole energy range; the techniques used in the measurements are also indicated. The spectra of protons and a particles alone are indicated belowabout 1012eV. At energies above this value the evidence as to the mass composition of the nuclei becomes increasingly vague. As indicated in the Figure, above about 1015eV the spectrum is derived from measurements on extensive air showers; these are essentially calorimetric and the total energy brought in by the primary nucleus is determined.
Figure 2 shows that the primary spectrum of all nuclei summed together can be written in the form j(E) ~ E-Y(E) where y(E) is approximatelY constant (at ~ 2.6) for 1010 < E < 3.l0l5eV and has a different value (~ 3.2) for E > 3.l0l5eV. In fact, the actual situation may be somewhat more complicated than this, as will be seen in a later Chapter.
Also shown in Figure 2 are the spectra of electrons and posi­ trons, and the diffuse y-ray spectrum; it was these spectra which gave rise to the energy densities given in Table I.
111. INTERACTIONS OF PRIMARIES IN THE GALAXY AND BEYOND
1. General Remarks
The previous section has dealt with the form of the energy spectrum of the various primary components. This information, together with such data as are available on the directional properties of the components, provides the basis on which origin theories arp. erected.
Clearly, a distinction must be made between the interactions for y-rays, which propagate in straight lines, and might be expected to give rather specific clues as to the origin and those for charged particles, which are subjected to the deflections caused by the various magnetic fields in space. In the following sections a brief analysis of the more important interactions will be given.
2. Interactions of Charged Particles
The interactions can be divided into those with magnetic fields, matter and with radiation. Figure 3 summarises the situation for protons and heavier nuclei
The relation in Figure 3 indicates that, in a typical galactic field of 5~gauss, a proton of momentum 1018eV/c has a Larmor radius of ~ 200 pc, i.e. about the half-thickness of the galactic disc in our vicinity. This means that at momenta much
INTRODUCTORY COSMIC RAYS
below this value (say ~ 1016 eV / c) the galactic field and i ts irregularities are likely to smear out the arrival directions of particles which may have been produced in specific galactic sources unless these sources are comparatively local. Only at much higher momenta will specific galactic sources be likely to stand out when 'viewed' with charged particles.
With m~n:.:.::e:..::ti=-c ...:cf,,:ie,,:ld! y-- ~c = 300 Bf
/3-- 15 / 10 eV for proton in
I~G and lparsec
gas ) 11"~ produelion
11
_v Z-~ as above plus ~ fragmentation
Fig. 3: Types of interaction of cosmic ray protons and nuclei.
Nucleons and nuclei interacting with interstellar gas atoms generate pions and the usual mixture of other secondaries (kaons, etc.) just as they do when they interact with the gas atoms in the earth's atmosphere. It is almost certain that the galactic y-rays referred to earlier originate in this way although whether the increased y-ray emissivity which appears to exist at ~5 kpc from the galactic centre comes from an increased rate of cosmic ray proton production in this region (e.g. Stecker et al., 1973), or whether it is due to an excess of gas there (molecular hydrogen etc.) is still an open question (Dodds et al., 1974). It is likely that some, at least, of the primary electrons and positrons (particularly those below 100 MeV) originate from the secondary y-rays.
7
The fragmentation process is an important one for understand­ ing the propagation of the cosmic ray components in the galaxy and many detailed studies have been made. From a knowledge of the relative numbers of the various secondary nuclei produced when heavy nuclei fragment, Shapiro et al. (1971 and later public­ ations) have used the measured primary composition to work back to the primordial composition, i.e. the relative numbers of
8 A. W. WOLFENDALE
nuclei. Figure 4 gives a brief summary of the situation, where the primordial abundances are given with respect to those in the solar photosphere. It should be rernarked that this area is one in which there is much contemporary activity: later Chapters give a more up to date account.
l00·u s? ..... I I ~ ~ 10·0
~
"
%?
Atomic runber
Fig. 4: The ratio of primordial cosmic ray abundances to those in the solar system (photosphere) plotted against atomic number, z. The figure is taken from the work of Shapiro et a1. (1971). Carbon is adopted as the datum. The ratios shown for hydrogen E and Rassurne that the primordial spectrum follows apower law in energy or rigidity respectively. U denotes the ratio for helium using measurements of solar spectra by Unsold (1969) and F denotes that from measurements by Biswas et al. (1966) of energetic solar particles. The shaded areas for heavy nuclei are based on the rneasurements of Fowler et al. (1970).
Turning to interactions with radiation fields, these are presumably of importance in the vicinities of sources; for example, ne ar pulsars the intense radiations will quickly cause fragmen­ tation of such heavy nuclei as may be initially accelerated to energies above threshold (threshold being such as to give photon energies as "seen" by the nucleus of several MeV). On the galactic scale the interactions with starlight and the black body radiation (2.7 K) are not serious because the interaction lengths are very long; however in extragalactic space they do achieve importance and this aspect is considered later.
Finally, concerning electrons in the galaxy, their low rnass
INTRODUCTORY COSMIC RA YS
causes interactions by way of bremsstrahlung, Inverse Compton effect and synchrotron radiation to be important. The more important ones, away from regions of high matter density, are the latter two and it can easily be shown that the degradation energy is severe above an energy E given by
c
of
where T is the lifetime in the region in question and W is the combined energy density of photons and magnetic field. Using the data of 11.2 gives W ~1.2 eV cm-3 • Independent measurements of T for electrons have not yet been made but there is some evidence for protons and nuclei, from the measured relative abundances referred to earlier, which suggest that the mean lifetime is 1014s (this value comes from a mean path length of 5 g cm-2 taken together with an assumed mean interstellar density of 1 atom cm-3). If electrons have the same mean life then the equation above gives E ~8.l0l0eV.
Wilh mal.., 'e.g. interstellar
starlight )
c
e-
Fig. 5: Types of interaction of photons
Although this is not the place to examine this point in detail it is interesting to note that the measured electron spectrum (Figure 2) does not show any signs of the expected more rapid fall above this value of Ec ; it is apparent that, unless the experimental data are inaccurate,either W or T is in error. It is probable that T is the culprit, i.e. that electrons and nuclei are not derived from the same sources and do not remain in the galaxy for the same length of time.
9
10
A.W.WOLFENDALE
Photons interact with matter and other photons in a variety of ways, the most important of which, are shown in Figure 5.
The photons interact with the material near their sources and the interstellar medium in general in a similar fashion to that of protons and nuclei. Confining attention to the inter­ stellar medium the photons with energy in the region of tens of eV have comparatively short ranges whereas above about 5 keV the photons can penetrate from outside the galaxy with little attenuation.
Fig. 6: Interaction length against photon energy for collisions of photons with photons of the various radiation fields (after Wdowczyk et al., 1972). The process concerned is e+e- production except where indicated otherwise.
The interaction length for proton - 2.7K black body photons is also shown (it is denoted P~BB)'
-2 -3 The adopted energy densities are: starlight, 10 eV cm infra-red, 2.4xlO-2eV cm-3 ; 2.7K, 2.4xlO-l eV cm-3 and radio, 5xlO-8eV cm-3
As mentioned earlier, photon-photon collisions are characterised by very long inter action lengths and are thus of much greater importance for propagation in extragalactic space. Figure 6 gives the variation of interaction length with photon energy for the photons in the various radiation fields; starlight,
INTRODUCTORY COSMIC RA YS
infra-red, 2.7K and radio. The assumed energy densities are indicated in the caption to the Figure. The attenuation 1engths can be viewed against the fo11owing dimensions:
21 thickness of ga1actic disc ~400pc ~ 10 cm. distance to ga1actic centre ~3.1022cm. 25 dimension of Supercluster of ga1axies ~6.10 cm.
C1ear1y, for energetic y-ray propagation within the Super­ cluster attenuation by way of interactions with the ambient radiation (principa11y 2.7K radiation) must be al10wed for.
At this stage, the interactions of protons with the extra­ galactic fields can also be mentioned. Figure 6 shows the situation for the most important interaction, that with the b1ack body radiation, in which pions are generated. It can be seen that as with the case of energetic photons, interactions on the scale of the Supercluster and beyond are of importance.
IV. SUMMARY
11
The previous sections have briefly reviewed the main proper­ ties of the various primary cosmic ray components, with particular reference to their energy spectra and energy densities. Some attention has also been given to the inter action processes experienced in the Ga1axy and beyond by both particles and y-rays. Later Chapters will deal with all these matters in much greater detail, with the object of deriving as many clues as possible as to the likely sources of the components.
REFERENCES
Balasubrahmanyan, V.K. and Ormes, J.F., Astrophys. J., 186, 109, 1973.
Biswas, S., Fichte1, C.E. and Guss, D.E., J. Geophys. Rev. Zl, 4071, 1966.
Blandford, G.E., Proc. 12th Int. Conf. on Cosmic Rays (Hobart; Univ. of Tasmania) l, 269, 1971.
Dodds, D., Strong, A.W., Wolfendale, A.W. and Wdowczyk, J., Nature, 1974 (in the press).
Fichtel; C.E., Roy. Soc. Meeting on Origin of Cosmic Rays, 1974 (in the press).
12 A.W.WOLFENDALE
Fow1er, P.H. et a1., Proc. Roy. Soc. A318, 1, 1970.
Meyer, P., Proc. 12th Int. Conf. on Cosmic Rays (Hobart; Univ. of Tasmania) rapporteur paper, 1971.
Shapiro, M.M., Si11berberg, R. and Tsao, C.H., Proc. 12th Int. Conf. on Cosmic Rays (Hobart; University of Tasmania) 1, 221, 1971.
Strong, A.W., Wdowczyk, J. and Wolfendale, A.W., J. Phys. A., l, 120, 1974.
Unso1d, A.O.J., Science, 163, 1015, 1969.
Wdowczyk, J., Tkaczyk, W. and Wolfendale, A.W., J. Phys. A. ~,
1419, 1972.
Wolfendale, A.W., Cosmic Rays at Ground Level, Ed. A.W. Wolfendale (The Institute of Physics, London) 1, 1973.
THE GALAXY AND INTERSTELLAR MEDIUM
J.L. Osborne
I INTRODUCTION
The purpose of this chapter is to describe the ga1actic setting for the propagation and possib1e origin of cosmic rays. A description of the overall structure and constituents of our Ga1axy is fo110wed by an account of the physica1 properties and distribution of the interstellar medium. An attempt is made to solve the problem of covering such a broad subject in abrief review by concentrating on those features which are judged to have a direct bearing on the origin and propagation of cosmic rays. Even so it is not feasible to support the text fully with references. A suggested reading list is therefore given at the end.
11 STRUCTURE OF THE GALAXY
1. Total Mass
The matter of the Galaxy is in the form of stars, dust and gas, distributed mainly in a flat disco The total mass of the Galaxy is 2.1011 M®. The greatest fraction of the matter is in its approximately 1011 stars. The total mass of gas in the form of atomic hydrogen, estimated from the 2lcm wavelength emission, is about 5 109 M®. In addition there is molecular hydrogen, helium and heavier elements, which may bring the'mass of gas up to 10% of the total mass of the Galaxy. As is shown below the ratio of gaseous to stellar matter varies greatly with distance from the galactic centre. The distribution of dust, on the other hand, is similar to that of gas. The smoothed space density in
J. L. Osbome and A. W. Wol[endale (eds.), Origin o[Cosmic Rays, 13-24. All Rights Reserved. Copyright © 1975 by D. Reidel Publishing Company, Dordrecht-Holland.
14 1. L. OS BORNE
dust is about 1% of that of the observed gas.
2. The position of the Sun
The sun lies within 12pc of the ga1actic plane (lpc = 3 . 09 1018cm). The centre of the Ga1axy is in the conste11ation Sagittarius at 265.60 R.A., - 28.9° dec. Its distance can be found by estimating the distance of RR Lyrae variable stars in the centra1 condensation. The current1y accepted va1ue of 10 kpc has an uncertainty of about 10%. (Prior to 1963 a va1ue of 8.2 kpc was wide1y used).
A system of Ga1actic Coordinates (longitude 1, 1atitude b) centred on the sun is used to give directions in the Ga1axy. The equator of the system is the ga1actic plane and 1 = 0° is the ga1actic centre. The earth's north pole points to 1 = 123.0°, b = 27 . 4°. With respect to the average motion of nearby stars the sun is moving at 20 km s-l towards 1 = 60° b = 24°.
·20
""" ·15
.\0
• 5
0
- 5
-'0
-'5
-20
-15 - 10 -s -10
Fig. 1: A cross-section of the Ga1axy showing the distribution of matter. (After Oort (1965».
THE GALAXY AND INTERSTELLAR MEDIUM 15
3. Distribution of Stars
In describing the structure of the Galaxy the coordinates, R, distance from the galactic centre, and Z, perpendicular distance from the plane are used. In Figure 1 a cross section of the Galaxy is given. The contours show the distribution of mass density in stars in units of the smoothed density near the sun. The diameter of the disc is about 30kpc and the sun is thus at 2/3 of the radius, from the centre. The black spots indicate the positions of globular star clusters projected on to the plane through the sun and the galactic centre. These, the oldest stellar systems, form a roughly spherical halo of radius l5kpc. The surface density of all stars projected on to the galactic plane, is strongly peaked towards the galactic centre. Beyond R = lkpc the surface density falls approximately as exp (-R/4kpc).
The Z-distribution of the various classes of stars and constituents of the interstellar medium differ one from another. The 'thickness' of the disc for a particular class is ,usually expressed as the equivalent thickness (2Z ) i.e. the total thick­ ness that the disc of the objects would hä~e if it were a slab of uniform density, or the distance between half-density points (2Z!). The relation between these depends of course on the form of the Z-distribution. For a gaussian Z! = 0.94 Zeq while for an exponential Z1 = 0.69Zeq . In what follows the word 'thickness' . 1· 2 2 lmp les Z!.
Class of Stars
70
160
480
700
380
125
Table I: The total thickness of the galactic disc for various classes of stars and for supernova remnants.
The thickness of the disc in the neighbourhood of the sun for some representative classes of stars are shown in Table I. The thick­ ness increases in the sequence from the young, I stars, through the solar type (G) to white dwarfs.
To date approximately 80 pulsars are known in the Galaxy and for each the dispersion measure, J ne dl cm-3 pc, has been
16 J.L.OSBORNE
found. The integral is along the line of sight to the pulsar and ne is the density of thermal electrons in the interstellar medium along that line. 1f the average value of ne is known the spatial distribution of pulsars foliows. The thickness of the pulsar disc in units of dispersion measure is approximately 9.6cm-3 ~c. The thickness quoted in Table I corresponds to ne = 0.025 cm- . (see below). The Z-distribution of pulsars need not correspond to that of their parent stars because they may have been formed with high velocities. With the above value of ne the observed pulsars lie within about 5kpc of the sun. The total number in the Galaxy is estimated to be between 105 and 106 •
The thickness of the disc of supernova remnants is also given. About 100 remnants have been identified by their radio emission (17 have optical counterparts). Using those from which independent estimates of the distance are available, an empirical relation between surface brightness and diameter is obtained. This is applied to all the remnants to obtain the spatial distribution (Milne 1970, 1lovaisky and Lequeux 1972). The radial surface density distribution is flat out to R = 8kpc, falls between 8 and l2kpc and is very low beyond l2kpc. For R<8kpc the disc of supernova remnants is half as thick as at the sun.
4. The Spiral Structure
Most external disc-shaped galaxies have a structure of a spherical or barred nucleus surrounded by spiral arms in varying degrees of development. The spiral tracers in these galaxies, at visual wavelengths, are 0 and B type stars, regions of ionised hydrogen gas and dust lanes. For our own Galaxy, because of absorption at visual wavelengths by dust (about 2.2 magnitudes per kpc in the plane) visual observations of the structure are limited to a few kpc. The large scale spiral structure is deduced from 2lcm radio emission from neutral hydrogen. The ground state of the hydrogen atom is split into 2 levels with the electron and proton spins either parallel or antiparallel. The transition gives radiation of a frequency l420.4MHz. The natural width of the line is negligible and it is possible to measure Doppler shifts down to 0.2 km s-l. The intensity of radiation of a given frequency, 1y,is usually expressed as a brightness temperature, TB = (c L/2V2 k) ly. 1f, over the 2lcm line profile, the optical thickness is much less than unity the brightness temperature is proportional to the column density of hydrogen atoms. 1f the motion of the gas about the galactic centre is purely rotational and the rotation curve of the Galaxy is known the distance of a portion of the gas can be deduced from its radial velocity. The rotation curve of the Galaxy, for R<Re , the solar radius, can be measured (in a given direction the maximum radial velocity is that of gas at R = Re sin 1). Outside Re it is
THE GALAXY AND INTERSTELLAR MEDIUM 17
deduced from a model of the Galaxy. Figure 2 shows such a curve. The rotational velocity in the neighbourhood of the sun is (250 + 38) km s-l in the direction 1 = 900 • The period of rota­ tion at the sun is thus 2.5 108 yr.
300 '(km/SI
o Ro R(kpcl o 5 10 15 20
Fig. 2: Rotation curve of the Galaxy, uncertainties are typically + 10% (After Lequeux 1969).
From 2lcm surveys, maps of the spiral structure can be built up. Figure 3 is a composite map showing the position of bright ridges of emission. The next outer arm to the sun is the Perseus arm at the next inner is the Sagittarius arm. The average pitch angle of the arms is 12.50 • The sun lies within the so-called Orion arm. Stellar and radio observations show this to have a pitch angle of 200 • It is apparently not a major arm but an off­ shoot of the Sagittarius arm. The form of the arms indicates that the Galaxy is of a type intermediate between Sb and Sc.
The central region of the Galaxy has a complex structure. An interpretation of the 2lcm data is shown in Figure 4. The inner, partial or complete, rings of neutral hydrogen are rotat­ ing and simultaneously expanding with the velocities shown. The present kinetic energy of expansion of the 3kpc arm is 1053 erg.
To produce this by a single explosion would require the eJ"ection of 10~ 107 yrs ago with a total energy of 3 1058 erg.
(1)
The nuclear disc of neutral hydrogen which has radius 500 pc is also expanding. It has within it a partial ring of molecular hydrogen. At the gala~tic centre is the radio source. Sag, A, a 6 pc diameter source of synchrotron emission. Infra-red radiation at 2.2 ~m indicates that the density of normal stars rises to 106 pc=3 within 1 pc of the galactic centre. It has been suggested that there is a massive black hole at the centre of the Galaxy. The observed motion of the gas sets an upper limit to its mass of 2 108 M .
11)
..I ,--
Fig. 3: A eomposite map of the outer spiral strueture of the Ga1axy from 21em data by Versehuur (1973). Inner arms are not shown beeause of the 1arge uneertainty intheir distanee. Key: K Kerr (1970), H = Henderson (1967), Wa = Wannier et a1 (1972), W = Weaver (1970), V = Versehuur.
Ear1ier radio surveys at high ga1aetie 1atitudes were interpreted as evidence for a halo of dimensions comparab1e to the vo1ume occupied by the globu1ar clusters containing magnetic field and relativistic electrons. Further surveys with improved angular resolution showed that a large proportion of the emission came from features in the galactic disco There is still some evidence for a 'radio disc' of approximate radius 10kpe and thiek­ ness up to 5 kpc.
The persistence of spiral strueture in galaxies in spite of the differential rotation can be aeeounted for by the density wave
THE GALAXY AND INTERSTELLAR MEDIUM
t TO WH
3 kpc AA~ 53kms' COUNTERPART p.O 2 cm-"
Fig. 4: Schematic diagram by Sanders and Wrixon (1973) of the centra1 region of the Ga1axy.
19
theory. The spiral tracers are produced due to the compression of the gas as it traverses the density wave. In the Ga1axy the rotationa1 velocity of the wave pattern, independent of R, wou1d be 13.5 km s-l kpc-1 (Lin 1970). At the solar position the wave then moves with about half the speed of the gas and stars. This accounts for the appearance of the dust 1anes on the inner side of the bright spiral arm. It wou1d take (3 to 10) 107 yr for the sun to traverse a density wave. The model requires an amplitude of variation of total mass surface density of 10% and an arm to inter arm gas density ratio of 5.
111 PROPERTIES OF THE INTERSTELLAR MEDIUM
1. Constitution of the Interstellar Medium
The interstellar medium consists of gas, dust and cosmic rays, which can be considered as far as the dynamics are con­ cerned to be a hot tenuous gas. The interstellar f1ux of non­ re1ativistic cosmic rays that can be important in heating and ionizing the gas cannot be measured direct1y because of the shie1ding effect of the solar wind. The chemica1 composition of the gas is, hydrogen 70%,he1ium 28%, heavier elements 2% by weight.
20 J. L. OS BORNE
The eommonly quoted figure for the gas density in the plane is 1 atom em-3 • The gas is either neutral-atomie, ionised or moleeular; these states and the variations in density are dis­ eussed below. The 'neutral' gas has a low level of ionisation (10-3) due to eosmie rays and photo-ionisation of Ca and Na atoms. This is suffieient to 'freeze' the magnetie field to the gas. The dust grains will also be eharged and tied to the field. The galaetie magnetie field is deseribed in the artiele by Thielheim. It appears to have a regular eomponent of strength 3uG lying along the loeal spiral arm, or spur, and an irregular eomponent of the same magnitude. The dust grains whieh have radii of the order of O.lum probably have no direet effeet on eosmie rays. The sugges­ tion that the soft X-ray background in the Galaxy is due to trans­ ition radiation from the grains eould only be true if there were a very large energy density (lOeV em-3) in low energy eosmie rays.
2. The Neutral Gas
The neutral gas, predominantly hydrogen, ean be termed HI • Beeause of the way that the rate of heating of the gas depends upon its density there are two stable phases of the gas: hot low density (nH< 10-1 em-3,T > 6000K) and cool high density (nH> 1 em-3,T < 300K). Observations are eonsistent with there being cool elouds in a hot intereloud medium. The following properties of 'standard elouds' are quoted: diameter 10pe, number along line of sight 5 kpe- l , density 8em-3 . It must be stressed however that the interpretation of the 2lem data in terms of such clouds is by no means unique. Ideally 6 spaee and velocity coordinates of the gas are needed to define a eloud while only the direetions (1 and b) and radial velocity (Vr ) in fact are known. For a given direetion the line TB(Vr ) is analysed into gaussian components and searehes are made for eorresponding eomponents in a line in an adjaeent direetion. Typieal interna 1 veloeities in the elouds are -1 km s-l while the 3 dimensional r.m.s. velocity of the clouds is -11 km s-l. The shape of the elouds, spheres or shells or sheets, is not known. Heiles (1967) has studied the eloud size speetrum. As weIl as a few 'standard' elouds he found many 'eloudlets' with radii 1 to 4 pe and densities·2 em-3 . From emission and absorption profiles the temperatures of the elouds are generally measured to be in the rang3 60K to 80K. Measurements of the intereloud medium give a few 10 K. Falgarone and Lequeux (1973) give the following figures for the solar neighbourhood. Density in the plane: (a) for the intereloud medium 0.16 em-3 (b) for a smoothed average of eloud material 0.29 em-3 • Thiekness of dise: (a) eloud and intercloud 360 pe (b) eloud only 310 pe (e) inter­ eloud only 550 pe. The value of 0.45 em-3 for the total density of neutral hydrogen is supported by satellite observations of the Lyman a profiles of stars. From measurements of absorption
THE GALAXY AND INTERSTELLAR MEDIUM 21
in the arm and inter arm regions along the line of sight to strong radio sources the arm-inter arm density ratio is estimated to be- 8.
A map showing the thickness of the disc of Hr gas (cloud and intercloud) by Jackson and Kellman (1973) is presented in figure 5. For 4.5 < R < 10 kpc the thickness is practically constant at -250 pc reducing to 100 pc closer to the centre. As can be seen the thickness increases rapidly beyond 10 kpc except for an anomalous region near 1 = 1400 • At high latitudes high velocity clouds are observed, the majority approaching the plane. These have been interpreted as material that is either condensing from the intergalactic medium or that is falling back after hav­ ing been ejected. The radial surface density distribution of Hr
" 230'
·'240'
-250'
-260'
-210'
_280'
330'
"\\\1/// / 220' 210' 200' 190' 180' 110' 160' ISO' '140'
340' 350' 0' 10' 20'
/ I 1 \ \
30'
\ Fig. 5: A contour map of the thickness (2Z!) of the Hr gas beyond R = 10 kpc (After Jackson & Kellman i973).
is shown in figure 6. This peaks at 13 kpc in strong contrast to the stellar distribution. The radial distribution of the volume density of Hr at Z = 0 peaks at about R = 8 kpc but the decrease beyond 8 kpc is compensated by the increasing thickness of the Hr disco
22 J. L. OSBORNE
3. Ionised Gas
Spheres of ionised hydrogen, (H11 regions), surround young, hot 0 and B type stars. The gas is 10nised comp1ete1y out to a shar~ly defined boundary. The radius of the sphere varies as nH-2 3:for an 05 star it is 100 pc when n = 1cm-3 • The HII regions can be seen optica11! or as thermal radio sources; the temperature of the gas is 10 K. It is possib1e that they act as sources of most of the kinetic energy of the neutral gas. 'Giant' HII regions (defined as those with 4 times the 1uminosity of the Or10n Nebu1a) indicate sites of star formation and are use­ fu1 as spiral tracers. The radial distribution of their density in the Ga1axy is shown in figure 6.
The mean density of thermal e1ectrons within a few kpc of the sun can be obtained from dispersion measures of pulsars whose distances are known independent1y, after discounting the effect
.~ I ... 0 Z~
:::t", ~ Cl: O.or'LLh'f'//.u;
OISTANCE FRQM GAL ACTIC CENTER (kpcl -
Fig. 6: Radial distributions of number density of giant H1I regions (Hatched) and surface density of HI • (After Mezger 1970).
of any HII region a10ng the 1ine of sight. Estimates in the range ne = 0.025 to 0.05 cm-3 have been obtained. The recombina­ tion rate of e1ectrons and ions is rough1y pro~ortiona1 to the square of the density. Thus at equi1ibrium ne oc nH' The thick­ ness of the e1ectron disc shou1d then be greater tha~ that of the neutral gas by a factor of 2 or 12 respective1y for an exponentia1 or gaussian Z-distribution. This is consistent with estimated va1ues of 800 to 1000 pc, derived from rotation measures of extraga1actic radio sources (Fa1garone and Lequeux (1973).
4. Mo1ecu1ar Hydrogen
Mo1ecu1ar hydrogen has no radio emission. It is possible that this 'invisible' hydrogen is an important constituent of the interstellar medium. A1though H2 cannot be direct1y photo­ dissociated by radiation of longer wave1ength than the Lyman limit
THE GALAXY AND INTERSTELLAR MEDIUM
there are indirect processes that limit nH2/nH in a 'standard' cloud to 10-5 • In dense dust clouds, however the interior is shielded and the hydrogen should be mainly molecular. Recent observations of emission from CO molecu1es imply a peak in the distribution of H2 at R = 5 kpc. This is very significant for the interpretation of y-ray data. Details are given in the article by Stecker.
SUGGESTED READING
"The Interstellar Medium" Ed. by K. Pinkau, NATO ASI Series C6 (D. Reidel) 1974).
"Diffuse Matter in Space" by L. Spitzer (Interscience) 1968.
"The Interstellar Medium" by S.A. Kaplan and S.B. Pikelner (Harvard Univ. Press) 1970.
"The Spiral Structure of Our Galaxy" LA.U. Symp. 38 Ed. by W. Becker and G. Contopoulos (D. Reidel) 1970.
"Interstellar Gas Dynamics" LA.U. Symp. 39 Ed. by H.J. Habing (D. Reidel) 1970.
REFERENCES
23
Ealgarone.E. and Lequeux, J., Astron. and Astrophys. Q, 253, 1973,
Heiles, C., Astrophys. J. Suppl. Sero l1, 97, 1967.
Henderson, A.P., Unpublished Ph.D. dissertation, University of Mary1and, 1967.
Ilovaisky, S.A. and Lequeux, J., Astron. and Astrophys. ~, 169, 1972.
Jackson, P.D. and Kellman, S.A., Astrophys. J., 190, 53, 1974.
Kerr, F.J., 'Spiral Structure of our Galaxy'(see above) p 95, 1970.
Lequeux, J., 'Structure and Evolution of Galaxies' (Gordon and Breach), 1969.
Lin, C.C., 'Spiral Structure of our Galaxy'(see above) p 377, 1970.
Mezger, P.G., 'Spiral Structure of our Galaxy' (see above) p 107, 1970.
24 J.L.OSBORNE
Mi1ne, D.K., Aust. J. Phys. 23, 425, 1970.
Oort, J.H., 'Ga1actic Structure' Ed. by A. B1aauw and M. Schmidt (University of Chicago) p 455, 1965.
Sanders, R.H. and Wrixon, G.T., Astron. and Astrophys. 26, 365, 1973.
Wannier, P., Wrixon, G.T., Wi1son, R.W., Astron. and Astrophys. ~, 224, 1972.
Weaver, H.F., 'Spiral Structure of our Ga1axy' (see above) p 126, 1970.
Verschuur, G.L., Astron. and Astrophys., ~, 73, 1973.
EXTRAGALACTIC COSMIC RAYS
I INTRODUCTION
In these lectures I shall largely be concerned with the view that the bulk of the primary cosmic rays is of extragalactic or~g~n. In order to set the stage for these ideas, a survey of the components of the extragalactic universe will be given. Then much of the discussion will centre about the various types of extragalactic non-thermal sourees.
Throughout the discussion we assume that the Rubble constant R 50 kms- 1 Mpc- 1
o
1. Condensed Objects
(a) Galaxies. The most important component which we are certain about is simply the galaxies. They are discrete objects and appear to comprise the major mass-energy contribution. In general, they have very strong clustering tendencies. The mass-energy density present in the ~niverse~ due to galaxies, using the above value of Ro ' is -10 31 g cm 3
The critical mass density r~~uired for a closed universe in which qo = 1/2 is Pcrit = 5 x 10 0 g cm- 3 (this is also the value required in the steady state cosmology). Thus, the closure density is about 50 times the "observed" value for galaxies, and if a closed universe is accepted, the question of the missing mass is raised. None of the other components that will be mentioned and
J. L. Osborne and A. W. Wolfendale (eds.), Origin of Cosmic Rays, 25-36. All Rights Reserved. Copyright © 1975 by D. Reidel Publishing Company, Dordrecht-Holland.
26 G. R. BURBIDGE
that are known to exist, give mass densities approaching that for galaxies. Some workers are therefore now suggesting, quite reasonably, that we may live in an open hyperbolic universe.
(b) Quasars (= Quasi-stellar objects [ QSOs ]). Quasars are also discrete objects which do exist and can be directly observed. It is not known what contribution they make to the mass density of the uni verse. There is an argument about their distances, but even if we could settle this, there is no direct way of measuring their masses. Gonsequently we do n~t know what contribution they could make, except to say that it is almost impossible that they make a very large contribution.
Large nurnbers have been detected through the radio a.nd optical surveys. The total number down to about 19~5 to 20m probably amounts to no more than about 10 6 • If they lie at cosmological distances, their space density is very low compared to that of galaxies. If they are comparatively local, their space density is very much higher, but there is every reason to believe that their masses are then quite small.
(c) Highly Evolved or Gollapsed Gonfigurations. A third contribution, for which we have no direct evidence, is that from various evolved or collapsed configurations. It is reasonable to suppose that some evolved galaxies and massive black holes are present. If we take the view that clusters of galaxies are bound relaxed systems, and this is likely for clusters like the Goma cluster, there must be a large amount of dark matter, because the kinetic energy of the visible galaxies is much greater than their potential energy. In one or two cases such as the Goma cluster it is difficult to argue that it is in any form other than collapsed or highly evolved matter.
(d) Faint Low Mass Stars. There mayaiso be a very large population of very faint low mass star systems, such as globular clusters. Some at distances of a few hundred kiloparsecs have been detected by accident. It is not obvious that they are satellites of our Galaxy or of the Andromeda nebula. Such inter­ galactic globular clusters could be distributed extensively throughout the universe. However, it is hard to believe that they could make a very large contribution to the total mass of the universe.
2. Diffuse Matter
We pass on to the diffuse gas present in the uni verse. We are only able to set certain limits on the mass of gas that may be present in intergalactic space. It was originally thought that, if the gas is present, it is likely to be in the form of cold
EXTRAGALACTIC COSMIC RA YS 27
atomic hydrogen, a reasonable notion if we accept the idea that the universe may have expanded from an initially hot dense state.
The 2l-cm line observations have been used to set a limit of < 10- 30 g cm- 3 on the density.of intergalactic matter. Attempts to detect the Lyman a absorption from quasars, assuming they are at cosmological distances, have set a lower limit of < 10-35 g cm- 3 •
lt can then be argued that, if one feels that there ought to be gas present, it must be hot gas, in which case one expects to see background bremsstrahlung X-rays. Some attribute part of the background X-ray flux to this, and it has been argued that one can reach the closure density in this way. lt is also possible that the background flux is the integration of discrete sourees. These sources may be clusters of galaxies, Seyfert galaxies or a new class of X-ray galaxies. lf clusters dominate, the X-rays may either be due to Compton scattering or from hot gas in the clusters. But in any case the discrete source explanation for the background if accepted necessarily means that no evidence is available on intracluster gas.
We have no idea how to estimate the contribution of inter­ galactic dust to the mass-energy of the universe, except to say that dust cannot form unless comparatively heavy elements are available (at least carbon) and this would seem to imply that there cannot be an appreciable contribution.
3. The Electromagnetic Fields
The energy density of starlight is estimated to be -10~35 g cm- 3 • (All energy densities of radiation will be quoted ~n mass units [1 eV cm- 3 = 1.8xlO-33 g cm- 3).) The contribution from the ultraviolet region is certainly not bigger than this by mor7 than a factor of ~ 10. The ultraviolet part of the electromagnet~c spectrum is one which has not been surveyed for faint discrete sources and it is likely that when this is done new classes of ,discrete ultraviolet sources will be discovered.
Radio waves contribute _10- 36 g cm- 3 due to the integration of the radio emission of all the discrete radio sources through­ out the universe. The X-ray and y-ray backgrounds are expected to contribute 10- 37 g cm- 3 • The microwave background is the
-33 -3 largest component _10 g cm This assurnes we are looking at a black-body spectrum of 2.7 K. The microwave measurements follow the black-body curve fairly weIl, but we may still be in for sur­ prises as we come down to the shorter wavelength side of the curve. A discrete source component may be present, making a comparatively minor contribution. lt is important to realise, however, that such a component would almost certainly arise from discrete non-
28 G. R. BURBIDGE
thermal sources. Such sources would therefore generate cosmic electrons and protons.
4. Neutrino Flux
The limits that can be set on the low-energy neutrino flux are exceedingly poor. The possibility that the bulk of the mass­ energy in the universe is due to neutrinos cannot be eliminated. The limits that can be set by looking at the end of the ß-decay spectrum are about a factor of 10 3 to 10 4 higher than the value corresponding to the closure density.
5. Gravitational Waves
If it is assumed that the gravitational wave phenomenon that Weber is discussing is real and that the gravitational waves come from our Galaxy, then if all galaxies are radiating in a similar fashion, it is clear that a very large amount of mass-energy is present in the universe in the form of gravitational waves.
Almost certainly some gravitational waves are present, and they do make a contribution. However, without definite results from the experimental standpoint, one cannot make definite arguments.
6. Cosmic Rays
The final component to be mentioned is cosmic rays. Here we can go from the extreme universal hypothesis which says that the energy density is 10- 33 g cm- 3 to the extreme non-universal hypothesis which says only the highest energy cosmic rays are extragalactic giving an energy density value as lowas 10- 37 g cm- 3 •
It is the generation of the cosmic rays in the galaxies and their interaction with some of the other components listed above that we shall be concerned with here.
111 RADIO SOURCES
1. Normal Galaxies
It is generally assumed that the detection of non-thermal radio sources teIls us that relativistic electrons are present and this is therefore apointer for cosmic ray physics. Where an electron component is present, it is reasonable to assume that there is also a proton component.
EXTRAGALACTIC COSMIC RA YS
In normal spiral ga1axies, 1ike our own, we see radio emission from the disk, and possib1y from more extended regions. Recent1y a number of spira1s have been studied with the high resolution Westerbork array (e.g. Van der Kruit, 1973) showing very interesting structures.
29
There are a number of e11iptica1 ga1axies which show compact, weak, radio sources in their nuc1ei. This phenomenon appears different from that found in the spira1s, in that in the e11ipti­ ca1s which show such continuum emission, it is in all cases con­ fined to their nuc1ei, and is associated with high excitation gas which is also confined to the nuc1eus. In general, not much gas is found in e11iptica1s (no 21-cm emission has ever been seen) which sets quite severe limits on the amount of neutral atomic hydrogen « 10-4 Mga1axy) in some of the nearest e11iptica1s. However, in some cases compact sources can be seen and this appears to be confined to the situation where there are comparative1y sma11 amounts of ionized gas. The e1ectron tempera­ ture is in the range 3 x 104 K to 4 X 104 K and optica1 1ines of the kind one wou1d expect (0 111, 0 11, N 11, S 11, Na V, etc.) are observed. The amount of gas that is excited ne'ed on1y be ~ 102 Mo, this ref1ects on the nuc1ear activity invo1ved on this comparative1y sma11 sca1e.
2. Powerfu1 Extended Sources
(a) Radio ga1axies with compact components. The powerfu1 radio sources tend to be double with the optica1 object (e11ipti­ ca1 ga1axy, N-system or QSO) 1ying between the two radio components. The ca1culations of the minimum total energy in the sources in the form of relativistic particles and magnetic flux gives values 1ying in the range ~ 10 58 _10 60 ergs. These are conservative estimates and require that there is rough equipartition between energy in partic1es and magnetic fie1d, i.e. Ep = (4/3)Em • For a 10ng time I have argued that equipartition is un1ike1y and that probab1y E »Em. Some of the strongest sources have been studied in detai1,Pand at high resolution. I sha11 very brief1y mention some of the individual cases which have been studied in detail. One of the newer resu1ts is that it is found that in quite a 1arge fraction of the double sources, a weak compact component is associated with the centra1 optica1 object. This shows that the violent activity is going on continuous1y.
NGC 1275 - Perseus AT. The ga1axy NGC 1275 is a strong radio source in the Perseus cluster. The radio emission from the cluster is extended and severa1 ga1axies appear to be invo1ved. The cluster
tIn the 1ectures, slides of this and other objects were shown.
30 G. R. BURBIDGE
also contains an extended X-ray source with possibly a compact component on NGC 1275. The extended X-ray source may be connected with the radio phenomenon, if indeed the X-rays are generated by the Compton effect and are not bremsstrahlung of hot gas. NGC 1275 has a Seyfert nucleus. This nucleus also contains a very compact, variable high-frequency radio source. The galaxy also lS
ejecting a large mass of gas at velocities ~ 3000 km s-l. The total kinetic energy in this gas alone is of the order of 1059 ergs.
NGC 5128 - Centaurus A. This is the nearest powerful extra­ galactic radio source to us, and it lies at a distance of about 4 Mpc. It is not impossible that some of the cosmic rays we observe at the earth are coming from this object. Photographs show a giant elliptical galaxy with a very broad dust band across it. The extended radio source is double, Hith a dimension 'V 800 kpc. There is an inner pair of small sources close to the optical object. Host re cent observations show there is an extremely small source in the nucleus of the galaxy. Thus a range of time scales of activity is apparent. There is also an X-ray source in the nucleus. The X-rays may be generated by the Compton collisions of radio electrons with the microwave radiation.
M87 = NGC 4486 - Virgo A. This source has an extended halo of radio emission. There is also an extended X-ray source. This galaxy contains the famous optical synchrotron jet and the weaker counterjet. In the nucleus a very tiny (high frequency) radio source with a dimension of only a few light months has been found. The existence of the jet indicates that fluxes of particles with energies in the 104 GeV range are being generated or reaccelerated continuously, Vlhile the compact radio source indicates that activity must be going on on time scales of months or years.
Cygnus A. This is the most powerful of the sources with small redshifts. It is a classical double, and the early calculat­ ions showed that it posed a severe energetic problem. Recently, Hargrave and Ryle (1974) have mapped it with high resolution at 5 GHz using the Cambridge 5-km telescope. There are a pair of extended radio sources reaching out to approximately 90 kpc from the central optical object. Both contain a bright compact source at the furthest point from the central object. Hargrave and Ryle calculate the minimum total energies, assuming equipartition between relativistic electrons and the magnetic field, to be 3 x 1057erg and 4 x 1057erg for the two compact components. The equipartition magnetic field is 3 x 104 gauss for both. The life­ times of the particles giving rise to the radio emission are 5 x 104 years and 4 -x 104 years, respectively. These lifetimes are very short indeed, much less than the light travel time from the central object. The authors concluded that there must be a continuous injection or re-acceleratiol1 of electrons with apower
EXTRAGALACTIC COSMIC RA YS 31
of 1045erg s-l. These equipartltlon magnetic fields are very large indeed, and it appears likely that the true values of the fields are much less. If this is the case, then the total energies go up accordingly. If the fields are ~ 10-6 gauss then the total energy in relativistic electrons will be about 5 x 1061 ergs. The particle lifetime will then be increased to ~ 108 years. However, the existence of the highly compact components suggests that they contain particle generators which are continuously active. Unless it is proposed that the mechanism generates elec­ trons only, radio sources such as these will be very powerful sources of primary cosmic rays.
(b) Large Radio Sources. Our understanding of extragalactic radio sources is not very good and the new observations suggest two things. One is that very compact sources exist at very con­ siderable distances from the places where they were generated. This raises many questions concerning the propagation of the particles. Secondly, from the observations of very large radio sources at Westerbork, we can now see that extragalactic cosmic rays, at least as far as the electron component is concerned, do exist and fill very large volumes of space, larger even than the usual volumes of clusters of galaxies. These last remarks are made following the discovery by Willis et al. (1974) of the faint and very extensive radio components of 3C 236 and DA 240. The dimensions of these sources are 5.7 Mpc and 2.0 Mpc,respec­ tively. The equipartition magnetic field strengths for both approach 10-6 gauss (assuming the energy of cosmic-ray protons to be negligible). The extended source 3C 236 contains a minimum energy in electrons of ~ 1060 ergs in a volume ~ 1074 cm3 . The electron energy density of ~ 10-14 erg cm- 3 is therefore similar to that in the disk of our Galaxy. The smaller source DA 240 has a slightly higher energy density of electrons. Despite their energy los ses (fur the parameters used here, Compton scattering is more important than synchrotron radiation) the electrons are able to propagate over very large distances. He are looking then at systems with electrons which are truly extragalactic, in the sense that the containment values are considerably larger than the volumes of clusters of galaxies.
3. Highly Compact Variable Sources
A third category of objects which are probably important particle generators are the extremely compact radio sources, Hhich are often found to be variable. Included here are the nuclei of galaxies, the BL Lacertae objects~ QSOs and N-systems. Their very small angular sizes (10- 4 and 10-j are seconds) imply linear dimensions of a few parsecs or less. Also if one argues that the light travel time across the objeet is less than the observed period of fluctuations, sizes of the order of light years are deduced. These scales do seem highly relevant to the whole phenom-
32 G. R. BURBIDGE
enon of explosive events in galaxies, uhether they involve multiple supernovae or the collapse of massive objects or some­ thing more exotic.
BL Lacertae itself was originally classified as a variable star. It is not a galaxy but may be a violent event superimposed on a galaxy*. It may be closer to the quasi-stellar phenomenon than any event we know. The number of objects of this type being discovered is increasing rapidly.
The simplest model that can be considered for the very com­ pact radio sources is a model in which one supposes there is a cloud of relativistic electrons and a magnetic field giving rise to an incoherent synchrotron source. Some part of the variability may be due to expansion of this cloud as was first proposed by Shklovsky for galactic supernova rernnants and by van der Laan for extragalactic sourees. In some cases there may be several such components. In the simplest case the radio spectrum of a non­ expanding source follows apower law, with a turn-over which·is almost certainly due to synchrotron self-absorption. If we make this assumption, the frequency of the turnover and the angular size of the source gives directly a measure of the magnetic field. From this one can look at the models and decide what are the energetics of a cloud of this type. It is found that in nearly all ca ses the energy in the particles, Ep , is very much greater than the energy in the magnetic field, Ern. (In general, as I described earlier, without knowing anything about the magnetic field, one assurnes Ep = Ern.) But in these cornpact sources a conservative estimate of the ratio Ep/Em ~ 104 to 106 (cf. Burbidge, Jones and O'Dell 1974). It turns out then, that in sources of this type one expects, in general, 1052 to 1056 ergs per outburst in relativistic electrons. It appears that nature has a way of making particles in a situation that is very far from equipart~t~on. Thus, outbursts occur on time scales of years or less, so that additively these types of sources are prolific generators of relativistic particles.
IV REQUlREMENTS FOR AN EXTRAGALACTIC THEORY OF COSMIC RAYS
I have concentrated so far on describing the properties of extragalactic non-thermal sources and in so doing I have shown that there is evidence that powerful generators of extragalactic cosmic rays exist. I now turn to a summary of the requirements for an extragalactic theory of cosmic-ray origin.
*Recent observations by Baldwin, Burbidge, Robinson and Wampler (1975), however, do not confirm the claim made recently by Oke and Gunn (1974) that a galaxy underlies the central object.
EXTRAGALACTIC COSMIC RA YS 33
By extragalactic origin, I mean the idea that the bulk of the energetic particles, i.e. the nucleons in the cosmic rays, come from outside the galaxy. These ideas have been developed in detail in the paper by Brecher and Burbidge (1972).
The requirements are summarized under several headings.
1. Cosmic Rays Outside the Galaxy
Evidence is required that cosmic rays exist outside the Galaxy with an energy density equal to that inside. We do not have this evidence. However, Ginzburg (1972) has proposed the test of looking for y-rays from nearby galaxies (from the Magellanic Clouds for example) which arise from the decay of neutral pions produced in pp collisions. He points out that if one does not find y-rays, it is evidence against extragalactic cosmic rays. If we do find y-rays, this does not necessarily mean it is evidence in favour, since the external galaxy may be a source of cosmic rays itself.
2. Evidence of the Existence of Powerful Extragalactic Cosmic Ray Sources
Evidence is required for the existence of powerful extra­ galactic sources of cosmic rays. If one accepts that the mechanism that gives rise to the radio emission is an incoherent synchrotron process, then such evidence does exist. I have summarized it in the previous lectures. Colgate has suggested an alternative mechanism in which the radio emission is produced by an oscillating plasma process. However, most of us believe at present that the synchrotron mechanism is responsible for most of the non-thermal radiation generated in the uni verse.
3. Evidence for the Escape of Cosmic Rays from Sources
As I have described earlier, evidence does exist that the electron component does escape from such sources, as electrons are found at very great distances from the places in which they must have originated. If protons are also gene~ated, they too will escape.
4. Energy Density Requirement
The energy density required for a completely universal theory is 10-12 erg cm- 3. The space density of galaxies is about one per 1075 cm3, so each galaxy must on average give rise to 1063 ergs in cosmic rays over a time scale of Ho-l (~ 1010 yrs). If each galaxy has a mass of 1011 M~, the rest mass energy is 2 x 1065 erg and about 0.5% of the rest mass energy of the galaxy must be converted by some mechanism into relativistic particles to give an energy
34 G. R. BURBIDGE
density of 10-12 erg cm-3. In view of the fantastic energetics that are observed, and the rate at which power is poured out in non-thermal processes in the universe, this number does not seem particularly unreasonable.
In the modified extragalactic theory (Brecher and Burbidge 1972), it was suggested that the cosmic rays cannot easily propagate over very large distances to fill the whole universe. Galaxies are largely confined to clusters, and if the view is taken that the propagation characteristics of extragalactic cosmic rays are such that they cannot travel distances greater than the dimensions of clusters in 109 to 1010 yrs, the overall energy requirements are reduced in the following sense: the clusters occupy only about 1% of the volume of space and our energy requirement is that one fills up only this volume. The require­ ment then becomes ~106l ergs per galaxy. The clusters will slowly fill up and the particles will spill out. Recent radio observat­ ions by Willis et al. (1974) are, however, against this notion. Cosmic electrons are present in volumes large compared with those occupied by clusters of galaxies. This may force one to return to the universal hypothesis. In the case of our own Galaxy, we are situated about 10 Mpc from the cent re of the Virgo cluster. We may lie on the edge of the supercluster, but in any case, if galac­ tic cosmic rays are extragalactic in origin and arise in systems like M87, they must have travelled 10 Mpc or more to reach uso As was mentioned earlier, closer objects like Centaurus A may contribute.
For the 3C radio sources the equipartition magnetic fields are 10-5 to 10-4 gauss and minimum energies are 1058_10 60 ergs. However, if the situation is far from equipartition with weaker magnetic fields, the energy in particles will be much greater. For example, if the assumed magnetic field is reduced by a factor of 10, the particle energy density is increased 30 times. To obtain a large extragalactic flux of particles, 107M® to 109M® per galaxy are required to be converted to relativistic particles. Whether these numbers are reasonable depends on our future under­ standing of galactic explosions. If electrons and protons are generated in each outburst in a fixed ratio such that Eprotonsl Eelectrons ~ 1, it is clear that while the electrons are rapidly reduced in energy by synchrotron los ses and Compton scattering, the proton flux will steadily build up.
5. Cosmic-Ray Propagation
Evidence is required that cosmic rays can propagate to us without being destroyed or giving rise to components which are not observed. For most energies of interest, electrons cannot propagate to us, since interaction with the universal radiation field will cut them off. Thus, ~oJe know that the electrons that we
EXTRAGALACTIC COSMIC RA YS
do see are largely Galactic in origin, and the extragalactic theory is for a nuclear component only.
An intergalactic proton flux will give rise to y-rays due
35
to collisions with the intergalactic gas. If the universe were closed, by the intergalactic gas, the predicted y-ray flux would be greater than that observed. However, as was described earlier, there is little evidence that there is an appreciable density of truly intergalactic gas, and there is no contradiction with observation at present.
6. Cosmic Rays Entering the Galaxy.
For an extragalactic theory we would like to have evidence that cosmic rays can enter the Galaxy. Parker (1973) has suggested that if the Galactic magnetic field configuration is closed, it could be difficult for cosmic rays to enter. He has also suggested that only sufficiently energetic cosmic rays (~ 1017eV) would be expected to enter. The field structure is not known, however, and there are explosive events which could blow holes in the magnetic field allowing particles to flow out. Certainly particles could then flow in.
I suspect that this problem, if it exists, is partly man­ made. So far, nearly all of the theoretical investigations have been made on the assumption that cosmic rays are Galactic and are trying to get out, not in. If the Galactic magnetic field structure is open, as it may be, particles will get in and flow through. Moreover, if we can show that the Galaxy is bathed in a sea of externally generated particles, I would have no doubt that they would eventually get in.
V. CONCLUSION
I have tried to make a reasonable case for the extragalactic cosmic-ray hypothesis, and to show you why someone like myself has been interested in it for a lang time. It started with the discovery of powerful extragalactic objects which, over the past 15 to 20 years, have been shown to be very important indeed. This theory has a similar genesis to the modern development of supernova origin theory which really started when Ginzburg, Shklovsky and PikeIner investigated the Crab Nebula and put forward the argument that he re was direct evidence for the generation of galactic cosmic rays. In my view, a similar case can be made for the extragalactic theory. Let us hope that the observations will enable us eventually to decide whether violent events inside our Galaxy, or outside are more important.
Extragalactic research at UCSD is supported in part by the
36 G. R. BURBIDGE
REFERENCES
Ba1dwin, J., Burbidge, E.M., Robinson, L. and Wamp1er, E.J., 1975, Ap. J. (Letters). To be pub1ished January, 1975.
Brecher, K. and Burbidge, G.R., 1972, Ap. J., 174, 253.
Burbidge, G.R., Jones, T.W. and O'Dell, S, 1974, Ap. J., 193, 43.
FeIten, J.E. and Morrison, P., 1966, Ap. J., 146, 686.
Ginzburg, V.L., 1972, Nature Physica1 Sciences, 239, 8.
Hargrave, P.J. and Ry1e, M., 1974, M.N.R.A.S., 166, 305.
van der Kruit, P.C., Astron. and Astrophys. 1973, ~, 249 and 263.
Oke, J.B. and Gunn, J.E., Ap. J. (Letters), 189, L5, 1974.
Parker, E.M., 1973, Ast. and Space Sei., 24, 279.
Wi11is, A.G., Strom, R.G. and Wi1son, A.S., 1974, Nature, 250, 625.
SIDEREAL DAILY VARIATIONS IN COSMIC RAY INTENSITY A1~ THEIR RELATIONSHIPS TO SOLAR MODULATION AND GALACTIC ANISOTROPIES
T. Thambyahpillai
Physies Department, Imperial College of Seienee and Teehnology, London SW7.
I. INTRODUCTION
From the earliest days of eosmie ray intensity reeording it has been reeognised that with a fixed instrument one eould use the spin of the earth to sear.. different parts of the sky and to measure anisotropieE by the diurnal periodie variations that should be indueed in the data. However, signifieant daily vari­ ations oeeur in both solar and sidereal times and beeause of the extreme eloseness of the two periodieities (365 solar days and 366 sidereal days in one earth year) one requires unbroken data spanning one eomplete year or preferably aseries of eomplete years in order to separate the two periodic variations. Even then a direet setting of the data in solar or sidereal time will not result in the separation of the solar or sidereal diurnal variations unless eaeh type of periodie variation retained a eonstant amplitude and phase throughout the year. This ean easily be seen by examining the situation on a harmonie dial. A harmonie dial is a method of representing a sinusoidal variation by means of a veetor and is a diagram in the form of a eloek-dial whieh is graduated in 24 hours for displaying diurnal variations. A veetor radiating from the eentre of the dial has a length equal to the amplitude of the sine wave and points to the time of day at whieh maximum intensity oecurs.
Let us eonsider the behaviour of a solar diurnal variation plot ted on a sidereal time dial. Let the data be sub-divided into 12 monthly groups and let the solar diurnal veetor for eaeh group be plotted on the dial. Beeause the solar eloek loses about 4 minutes per day or about 2 hours per month relative to the sidereal eloek the solar veetors for sueeessive months will
J. L. Osborne and A. W. Wol[endale (eds.), Origin o[ Cosmic Rays, 37-59. All Rights Reserved. CopYright © 1975 by D. Reidel Publishing Company, Dordrecht-Holland.
38 T. THAMBY AHPILLAI
rotate clockwise, the angular separation between successive vectors being 300 • Let us consider the special ca se in which the solar vector retains a constant amplitude and phase throughout the year. Here we can select pairs of months which are six months apart such as January and July, February and August and so on and find that these pairs have equal amplitude and are diametrically opposed to each other. Hence if we find the average variation in sidereal time over the year the six pairs will average to zero. If, however, the amplitude and/or the phase did not remain constant throughout the year, the average of the 12 monthly vectors will not reduce to zero. Thus, it appears that if there is an annual variation in amplitude and/or phase of the solar diurnal variation, this will result in the generat­ ion of a spurious diurnal variation in sidereal time and vi ce versa. Therefore, one has to isolate and eliminate spurious sidereal variations of solar origin be fore one can relate the remaining sidereal variation (if any) to an anisotropy of galactic cosmic rays. The theoretical methods necessary for tackling this problem are already available in radio communicat­ ions theory and were first adapted for the cosmic ray field by Farleyand Storey (1954). It is well known that a radio frequency carrier which is amplitude modulated by an audio­ frequency can give rise to signals at the carrier frequency as well as at two side-bands which correspond to the sum and difference of the radio and audio frequencies. In the cosmic ray case, the solar diurnal variation corresponds to the carrier and when amplitude modulated at the rate of one cycle per year gives rise to variations in the sidereal (366 cycles per year) and anti-sidereal (364 cycles per year) side-bands. In a similar way one can show that phase modulation of the solar diurnal variation would generate appreciable variations in aseries of side-bands falling on either side of the carrier and differing from the carrier by an integral multiple of the one cycle per year frequency. The important difference between amplitude and phase modulations appears to be that whereas only two side-bands are excited by amplitude modulation, aseries of side-bands should be excited by phase modulation. Our analysis of data from equipment located at sea-level as well as at moderate depths underground shows that no significant variations are observable outside the anti-sidereal and sidereal side-bands suggesting that phase modulation is not an important phenomenon in cosmic ray diurnal variations and hence we shall not consider phase modulat­ ion any further. Although Farley and Storey considered one component of the solar diurnal variation which undergoes an annual amplitude modulation, their method can very easily be adapted to cover the more general case of two components, one of which is due to atmospheric temperature changes and the other caused by primary anisotropy. We shall now consider this adap­ ted version of the Farley and Storey analysis.
SlDEREAL DAIL Y VARIATIONS IN COSMIC RA Y INTENSITY
II. THE MODIFIED FARLEY AND STOREY ANALYSIS
We sha11 use the subscripts atm and ani to denote the atmospheric and anisotropic components respective1y of the solar diurnal variation. Let A represent the annua1 mean amplitude and 8 the depth of modulation. It will be assumed that both solar components undergo amplitude modulation. It is convenient to measure time t in units of 1 year and let N denote the number of solar days per year. The percentage changes of cosmic ray intensity I can then be represented by the equation:
39
100 81 A (1 + 8 cos (27Tt - <I> )) cos (27TNt -.<1> ) I atm atm atmy atm
+ Ä , (1 + an1 8 ,COS(27Tt - <I> ,)) COS(27TNt - <I> ,) an1 an1Y an1
+ A 'd S1
This can then be reso1ved into components in solar, siderea1 and anti-siderea1 times as fo11ows:
Solar component = Ä COS(27TNt - <I> ) atm atm + A ,COS(27TNt- '" ) an1 ~ani
Siderea1 component = Asid cos (27T(N+1)t - <l>Sid»)
+ lÄ 8 cos [27T(N+1)t- (<I> + <l>atmy»)+ 2 atm atm atm
+ ~A , eS ani cos (21T(N+1)t- (<I> ,+ <I> ')) an1 an1 an1Y
Anti -s iderea1 component
!Äatm 8 cos (271 (N-1) t - (<I> - <l>atmy) J atm atm
+!Ä , 8 ani
cos (21T(N-1) t - (<I>ani - <I> aniy) J an1
The important re1ationships which Far1ey and Storey pointed out can be i11ustrated by considering one of the components, say the atmospheric,subject to amplitude modulation. First1y, the amp1itudes of the spurious siderea1 and anti-sidereal variations are equal. Second1y, the phase constants (<I>atm + <l>atmy) for the siderea1 and (<I>atm - <l>atmy) for the anti-siderea1 variations show that the two vectors are symmetrical about the generating solar vector with a phase constant <l>atm' Thus the corresponding
40 T. THAMBY AHPILLAI
spurious sidereal vector can be determined by 'reflecting' the anti-sidereal vector in the solar vector. A similar symmetrical relationship obtains with regard to the anisotropic component of the solar vector. Unfortunately, when we combine the two solar components and the two anti-sidereal components, this symmetrical relationship no longer exists as far as the resultants are con­ cerned unless very special circumstances prevail. It is therefore regrettable that some workers continue to apply the Farley and Storey correction to the observed (resultant) vectors without studying the suitability of the method in any particular case and there is sorne danger that the results so obtained may not be quite correct. It may therefore be worth­ while to examine briefly the possible ways in which the various components of the solar diurnal variation arise.
III. THE ORIGIN OF THE SOLAR DIURNAL VARIATION
As seen earlier, a solar diurnal variation can originate partly from atmospheric causes and partly from an anisotropy existing outside the earth's magnetosphere. The effects which fall within the first category are the barometer effect, the muon decay or negative temperature effect and the positive temperature effect, the last arising from a competition between capture and decay processes of the pion. Two types of aniso­ tropy following solar time are known, viz. the co-rotation anisotropy and the earth's orbital motion anisotropy. These effects will be examined in greater detail in the fo11owing, mainly with a view to fami1iarising the reader with the magnitudes of the variations involved.
1. The Atmospheric Effects
(a) The Barometer Effect. This describes the changes of cosmic ray intensity associated with changes in atmsopheric pressure. This effect arises part1y as a mass absorption effect and partly from the finite life-time of the muon. The barometer coefficient can be calculated if the muon momentum spectrum and the rate of energy loss in the air are known. (Dutt and Thambyahpillai, 1965). Using the readings from a barograph, the effects of pressure changes can be easily eliminated from the data.
(b) The Muon Decay Effect. Muons are believed to be produced mainly near the 100 mb pressure level and have to travel from the point of production to the recorder at sea-L~vel or underground without decaying. If the atmospheric temperature increases, the muons have to travel a longer distance in order to reach the recording instrument and thus a lower muon intensity is recorded because of a larger number of muons decaying in
SIDEREAL DAIL Y VARIATIONS IN COSMIC RA Y INTENSITY
flight. The decay coefficient is about 3.5% per Km. for a sea­ level recorder and has decreased to 0.7% per Km. for a recorder at a depth of 60 metres water equivalent (m.w.e. underground). It diminishes still further as the depth of observation
41
increases. In order to calculate the diurnal variation caused by the decay effect, it is necessary to know the diurnal variation in atmospheric temperature throughout the atmosphere. It is this information that is usually either not available or, if available, is open to serious doubts about its reliability. These doubts arise because in atmospheric soundings made during daylight hours there is uncertainty as to whether the readings given by the temperature elements reflect the true atmospheric temperature or some higher temperature produced by the absorption of solar radiation. However, indirect methods have been devised to estimate the annual mean diurnal temperature effect in sea-level muon data and these suggest that the temperature vector has an amplitude of about 0.1% and a time of maximum around 06 hr. Some estimates made on the basis of radio-sonde data give a vector which has a nearly double amplitude and a phase different from the previously given value by 4 hours. By using the indirect estimate, one can deduce that the temperature vector for a recorder at 60 m.w.e. depth yielded by the muon decay effect should have an amplitude of 0.02%. The vector would be still smaller at larger depths underground.
(c) The Positive Temperature Effect. This effect occurs only in the upper atmosphere weIl above the 200 mb. pressure level and as mentioned earlier arises because of the competition between decay and nuclear capture of the pions. At any pressure level, an increase in atmospheric temperature reduces the density and thus reduces the probability of nuclear capture. The decay probability is increased resulting in more muons reaching the detector. Thus a positive correlation between recorded muon intensity and stratospheric temperature results and this gives the effect the name of positive temperature effect. This effect cannot be calculated accurately because the absorption length of the pion may not be known precisely. Making simplifying assump­ tions, Trefall (1955) obtains the expression for the positive coefficient applicable to muons of energy E as
E 1 E + Eo T
where E is about 80 GeV and T represents stratospheric temper­ ature. °For observations at any particular depth, this expression has to be weighted using the muon energy spectrum but it is clear that the positive coefficient increases with increasing muon energy until is asymptotically approaches the value of 0.46% per oe. It is worthy of note that this effect, unlike the two effects described earlier, increases with increas-
42 T. THAMBY AHPILLAI
ing depth. Beeause the present trend is to make observations at greater depths underground than hitherto, it shou1d be stated that this atmospherie effeet ean eontribute to the observed solar diurnal variation and possib1y add a spurious eomponent in the siderea1 side-band at these greater depths. Onee again, the amplitude of the diurnal variation generated by the positive effeet eannot be ea1eu1ated direet1y beeause of the lack of re1iab1e information about atmospherie temperature ehanges.
2. Solar Diurnal Anisotropies
There are two known effeets whieh give rise to anisotropie distriubtions whieh fo11ow solar time. These ean be ea11ed the co-rotation anisotropy and the oribiau motion effeet. These will now be eonsidered in brief in the fo11owing:
(a) The Co-rotation Anisotropy. In order to maintain a fixed number of eosmie ray partie1es of a rigidity P in the inner solar system, the number of eosmie rays eonveeted out radia11y by the solar